The Geometry Of Intelligence: From Form To Formation - Towards A Predictive Science Of Intelligence

Can mathematics predict how intelligence develops? Biological brains and artificial intelligence systems can acquire similar capabilities despite their very different physical structures. Yet even systems trained on identical tasks can develop different internal computational organisations. Why? Mathematical theories can identify which computational structures are possible, but they do not necessarily explain why learning produces some structures rather than others. The Geometry of Intelligence: From Form to Formation examines whether mathematical principles can help bridge this gap, moving from describing the structures of intelligence to predicting how they emerge. Drawing on neuroscience, learning theory and biological pattern formation, the paper proposes a framework distinguishing what is computationally possible, what learning can reach, what is likely to emerge and what a particular system actually develops. Crucially, it sets out how such explanations should be tested: through prospective predictions, measurable organisational differences and comparisons with competing accounts. The broader question extends beyond today's artificial intelligence. Could transferable mathematical relationships eventually help us understand and anticipate the development of intelligence in biological, artificial and future hybrid systems? The paper offers a theoretical framework and practical criteria for investigating that possibility, while identifying what remains to be demonstrated.